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Asymptotically Optimal Estimation of Smooth Functionals for Interval Censoring,Case 2 and Beyond

机译：区间删失，情形2及其后的光滑泛函的渐近最优估计

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Estimation in the interval censoring model is considered. A class of smoothfunctionals is introduced, of which the mean is an example. The asymptotic information lower bound for such functionals can be represented as an inner product of two functions. In case 1, i.e. one observation time per unobservable event time, both functions can be given explicitly. We mainly consider case 2, with two observation times for each unobservable event time, in the situation that the observation times can not become arbitrarily close to each other. For case 2, one of the functions in the inner product can only be given implicitly as solution to a Fredholm integral equation. We study properties of this solution and prove that the nonparametric maximum likelihood estimator of the functional asymptotically reaches the information lower bound.

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